# Properties

 Modulus $1850$ Structure $$C_{4}\times C_{180}$$ Order $720$

Show commands: PariGP / SageMath

sage: H = DirichletGroup(1850)

pari: g = idealstar(,1850,2)

## Character group

 sage: G.order()  pari: g.no Order = 720 sage: H.invariants()  pari: g.cyc Structure = $$C_{4}\times C_{180}$$ sage: H.gens()  pari: g.gen Generators = $\chi_{1850}(1777,\cdot)$, $\chi_{1850}(1001,\cdot)$

## First 32 of 720 characters

Each row describes a character. When available, the columns show the orbit label, order of the character, whether the character is primitive, and several values of the character.

Character Orbit Order Primitive $$-1$$ $$1$$ $$3$$ $$7$$ $$9$$ $$11$$ $$13$$ $$17$$ $$19$$ $$21$$ $$23$$ $$27$$
$$\chi_{1850}(1,\cdot)$$ 1850.a 1 no $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$ $$1$$
$$\chi_{1850}(3,\cdot)$$ 1850.ch 180 no $$-1$$ $$1$$ $$e\left(\frac{41}{180}\right)$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{41}{90}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{107}{180}\right)$$ $$e\left(\frac{109}{180}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$
$$\chi_{1850}(7,\cdot)$$ 1850.bn 36 no $$-1$$ $$1$$ $$e\left(\frac{31}{36}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{7}{12}\right)$$
$$\chi_{1850}(9,\cdot)$$ 1850.bz 90 no $$1$$ $$1$$ $$e\left(\frac{41}{90}\right)$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{11}{30}\right)$$
$$\chi_{1850}(11,\cdot)$$ 1850.bl 30 no $$1$$ $$1$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$e\left(\frac{8}{15}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$
$$\chi_{1850}(13,\cdot)$$ 1850.cc 180 no $$1$$ $$1$$ $$e\left(\frac{107}{180}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{11}{90}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{47}{60}\right)$$
$$\chi_{1850}(17,\cdot)$$ 1850.cf 180 no $$1$$ $$1$$ $$e\left(\frac{109}{180}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{7}{30}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{73}{90}\right)$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{7}{90}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{49}{60}\right)$$
$$\chi_{1850}(19,\cdot)$$ 1850.ce 180 no $$-1$$ $$1$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{7}{45}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{143}{180}\right)$$ $$e\left(\frac{91}{180}\right)$$ $$e\left(\frac{41}{180}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{1850}(21,\cdot)$$ 1850.ca 90 no $$1$$ $$1$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{5}{9}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{11}{90}\right)$$ $$e\left(\frac{7}{90}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{4}{15}\right)$$
$$\chi_{1850}(23,\cdot)$$ 1850.bw 60 no $$1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{1850}(27,\cdot)$$ 1850.bv 60 no $$-1$$ $$1$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{11}{30}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{47}{60}\right)$$ $$e\left(\frac{49}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{1}{20}\right)$$ $$e\left(\frac{1}{20}\right)$$
$$\chi_{1850}(29,\cdot)$$ 1850.by 60 no $$-1$$ $$1$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{1}{10}\right)$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{13}{60}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{17}{20}\right)$$ $$e\left(\frac{3}{5}\right)$$
$$\chi_{1850}(31,\cdot)$$ 1850.bi 20 no $$-1$$ $$1$$ $$e\left(\frac{3}{10}\right)$$ $$1$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{9}{10}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{3}{10}\right)$$ $$e\left(\frac{3}{20}\right)$$ $$e\left(\frac{9}{10}\right)$$
$$\chi_{1850}(33,\cdot)$$ 1850.cg 180 no $$-1$$ $$1$$ $$e\left(\frac{89}{180}\right)$$ $$e\left(\frac{19}{36}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{173}{180}\right)$$ $$e\left(\frac{151}{180}\right)$$ $$e\left(\frac{13}{90}\right)$$ $$e\left(\frac{1}{45}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{29}{60}\right)$$
$$\chi_{1850}(39,\cdot)$$ 1850.ce 180 no $$-1$$ $$1$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{180}\right)$$ $$e\left(\frac{17}{180}\right)$$ $$e\left(\frac{67}{180}\right)$$ $$e\left(\frac{19}{90}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{7}{15}\right)$$
$$\chi_{1850}(41,\cdot)$$ 1850.ca 90 no $$1$$ $$1$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{31}{45}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{37}{90}\right)$$ $$e\left(\frac{89}{90}\right)$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{8}{15}\right)$$
$$\chi_{1850}(43,\cdot)$$ 1850.g 4 no $$1$$ $$1$$ $$-i$$ $$-i$$ $$-1$$ $$-1$$ $$-1$$ $$1$$ $$-i$$ $$-1$$ $$-1$$ $$i$$
$$\chi_{1850}(47,\cdot)$$ 1850.bu 60 no $$-1$$ $$1$$ $$e\left(\frac{17}{60}\right)$$ $$e\left(\frac{7}{12}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{29}{60}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{13}{15}\right)$$ $$e\left(\frac{7}{20}\right)$$ $$e\left(\frac{17}{20}\right)$$
$$\chi_{1850}(49,\cdot)$$ 1850.bc 18 no $$1$$ $$1$$ $$e\left(\frac{13}{18}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{2}{9}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{1}{6}\right)$$
$$\chi_{1850}(51,\cdot)$$ 1850.y 12 no $$-1$$ $$1$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{1}{3}\right)$$ $$e\left(\frac{2}{3}\right)$$ $$-1$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{1}{12}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$-i$$ $$-1$$
$$\chi_{1850}(53,\cdot)$$ 1850.cg 180 no $$-1$$ $$1$$ $$e\left(\frac{61}{180}\right)$$ $$e\left(\frac{11}{36}\right)$$ $$e\left(\frac{61}{90}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{157}{180}\right)$$ $$e\left(\frac{59}{180}\right)$$ $$e\left(\frac{17}{90}\right)$$ $$e\left(\frac{29}{45}\right)$$ $$e\left(\frac{31}{60}\right)$$ $$e\left(\frac{1}{60}\right)$$
$$\chi_{1850}(57,\cdot)$$ 1850.br 36 no $$1$$ $$1$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{17}{36}\right)$$ $$e\left(\frac{11}{18}\right)$$ $$e\left(\frac{5}{6}\right)$$ $$e\left(\frac{7}{18}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{29}{36}\right)$$ $$e\left(\frac{5}{18}\right)$$ $$e\left(\frac{1}{6}\right)$$ $$e\left(\frac{5}{12}\right)$$
$$\chi_{1850}(59,\cdot)$$ 1850.ce 180 no $$-1$$ $$1$$ $$e\left(\frac{13}{45}\right)$$ $$e\left(\frac{1}{18}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{1}{30}\right)$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{133}{180}\right)$$ $$e\left(\frac{31}{90}\right)$$ $$e\left(\frac{37}{60}\right)$$ $$e\left(\frac{13}{15}\right)$$
$$\chi_{1850}(61,\cdot)$$ 1850.cd 180 no $$-1$$ $$1$$ $$e\left(\frac{49}{90}\right)$$ $$e\left(\frac{7}{9}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{29}{30}\right)$$ $$e\left(\frac{11}{180}\right)$$ $$e\left(\frac{7}{180}\right)$$ $$e\left(\frac{107}{180}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{53}{60}\right)$$ $$e\left(\frac{19}{30}\right)$$
$$\chi_{1850}(63,\cdot)$$ 1850.bu 60 no $$-1$$ $$1$$ $$e\left(\frac{19}{60}\right)$$ $$e\left(\frac{5}{12}\right)$$ $$e\left(\frac{19}{30}\right)$$ $$e\left(\frac{1}{5}\right)$$ $$e\left(\frac{43}{60}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{9}{20}\right)$$ $$e\left(\frac{19}{20}\right)$$
$$\chi_{1850}(67,\cdot)$$ 1850.ch 180 no $$-1$$ $$1$$ $$e\left(\frac{119}{180}\right)$$ $$e\left(\frac{25}{36}\right)$$ $$e\left(\frac{29}{90}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{113}{180}\right)$$ $$e\left(\frac{31}{180}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{59}{60}\right)$$
$$\chi_{1850}(69,\cdot)$$ 1850.ce 180 no $$-1$$ $$1$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{17}{30}\right)$$ $$e\left(\frac{113}{180}\right)$$ $$e\left(\frac{121}{180}\right)$$ $$e\left(\frac{11}{180}\right)$$ $$e\left(\frac{77}{90}\right)$$ $$e\left(\frac{59}{60}\right)$$ $$e\left(\frac{11}{15}\right)$$
$$\chi_{1850}(71,\cdot)$$ 1850.bs 45 no $$1$$ $$1$$ $$e\left(\frac{44}{45}\right)$$ $$e\left(\frac{1}{9}\right)$$ $$e\left(\frac{43}{45}\right)$$ $$e\left(\frac{4}{15}\right)$$ $$e\left(\frac{38}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{26}{45}\right)$$ $$e\left(\frac{4}{45}\right)$$ $$e\left(\frac{14}{15}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1850}(73,\cdot)$$ 1850.be 20 no $$-1$$ $$1$$ $$e\left(\frac{17}{20}\right)$$ $$-i$$ $$e\left(\frac{7}{10}\right)$$ $$e\left(\frac{4}{5}\right)$$ $$e\left(\frac{19}{20}\right)$$ $$e\left(\frac{13}{20}\right)$$ $$e\left(\frac{2}{5}\right)$$ $$e\left(\frac{3}{5}\right)$$ $$e\left(\frac{11}{20}\right)$$ $$e\left(\frac{11}{20}\right)$$
$$\chi_{1850}(77,\cdot)$$ 1850.ch 180 no $$-1$$ $$1$$ $$e\left(\frac{23}{180}\right)$$ $$e\left(\frac{13}{36}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{7}{15}\right)$$ $$e\left(\frac{161}{180}\right)$$ $$e\left(\frac{127}{180}\right)$$ $$e\left(\frac{8}{45}\right)$$ $$e\left(\frac{22}{45}\right)$$ $$e\left(\frac{23}{60}\right)$$ $$e\left(\frac{23}{60}\right)$$
$$\chi_{1850}(79,\cdot)$$ 1850.ce 180 no $$-1$$ $$1$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{17}{18}\right)$$ $$e\left(\frac{28}{45}\right)$$ $$e\left(\frac{23}{30}\right)$$ $$e\left(\frac{167}{180}\right)$$ $$e\left(\frac{139}{180}\right)$$ $$e\left(\frac{29}{180}\right)$$ $$e\left(\frac{23}{90}\right)$$ $$e\left(\frac{41}{60}\right)$$ $$e\left(\frac{14}{15}\right)$$
$$\chi_{1850}(81,\cdot)$$ 1850.bs 45 no $$1$$ $$1$$ $$e\left(\frac{41}{45}\right)$$ $$e\left(\frac{4}{9}\right)$$ $$e\left(\frac{37}{45}\right)$$ $$e\left(\frac{1}{15}\right)$$ $$e\left(\frac{17}{45}\right)$$ $$e\left(\frac{19}{45}\right)$$ $$e\left(\frac{14}{45}\right)$$ $$e\left(\frac{16}{45}\right)$$ $$e\left(\frac{11}{15}\right)$$ $$e\left(\frac{11}{15}\right)$$